It is common for the paper used for printing magazines to vary significantly location to location, lot to lot, vender to vender. Less frequently, ink may also shift in color properties. For very color critical jobs, the client whose job is bring printed may be obliged to personally view and sign-off on the color appearance of a job, due to moderate changes in color of paper or inks. Virtual proofing has the potential to enable a remote “color sign-off”. However, one thing that is lacking from virtual proofing is the ability to predict how a color shift in one component such as paper or one of the CMYK inks will impact all the other colors which may be printed.
In the event of a paper or ink change, conventional techniques require measurements of large numbers of color patches to calculate and re-calculate color profiles. If the paper or ink changes, conventional wisdom mandates the re-calculation of color profiles, if color accuracy is needed. Moreover, many graphic design applications, like Adobe Illustrator™, do not accurately predict color output for overlapping similar transparent colors. This shortcoming is due to conventional graphic design applications' use of only CIELAB data when making their color predictions. For example, a graphic designer using a product like Adobe™ Illustrator™ may draw a logo or design using spot colors such as Pantone™. The graphic designer may choose to overlap different colored objects, enabling a “transparency” function of the graphic design application. If the colors are very different, such as yellow and cyan, the mixed result may look reasonable on display, as shown in FIG. 1. However, as shown in FIG. 2, if the two colors are identical or nearly identical (such as two cyans of slightly different shades) the overlapping region between the circles may look similar to each of the two circles, rather than appearing darker and more saturated, as one might expect. As can be seen, the addition of two colors each similar to Cyan=100% results in a color which is also essentially Cyan=100%, rather than a new color “Dark Cyan”=100%. This is because with only CIELAB data available, no estimate has been available for performing a more valid prediction.
Although algorithms have existed for many years for calculating resulting colors from mixing paints, dyes, etc., these algorithms have not been applicable to graphic design application. Generally, these calculations have been spectrally-based, meaning that full spectral information is required regarding both colorants and substrates in order to predict how they would add together to create a resulting color. For example, the Kubelka-Munk equation (Yang 2002) defines reflectance for multiple colorants on a paper substrate, where the colorants have both an absorption coefficient (k(λ)) and a scattering coefficient (s(λ) as a function of wavelength λ.
            R      a        ⁡          (              λ        ,                  z          q                    )        =                              (                                    R              ∞                        -                          R              g                                )                ⁢                  ⅇ                                    -                              (                                                      1                    /                                          R                      ∞                                                        -                                      R                    ∞                                                  )                                      ⁢            sz                              -                        R          ∞                ⁡                  (                      1            -                                          R                g                            ⁢                              R                ∞                                              )                                                          R            ∞                    ⁡                      (                                          R                ∞                            -                              R                g                                      )                          ⁢                  ⅇ                                    -                              (                                                      1                    /                                          R                      ∞                                                        -                                      R                    ∞                                                  )                                      ⁢            sz                              -              (                  1          -                                    R              g                        ⁢                          R              ∞                                      )            where Rg (λ) is the reflectance of the paper substrate, z is the colorant thickness, s is the same as the s(λ function, and R∞ (λ) is the reflectance of an infinitely thick colorant, calculated as follows:
      R    ∞    =      1    +                  k        ⁡                  (          λ          )                            s        ⁡                  (          λ          )                      -                                        (                                          k                ⁡                                  (                  λ                  )                                                            s                ⁡                                  (                  λ                  )                                                      )                    2                +                  2          ⁢                                    k              ⁡                              (                λ                )                                                    s              ⁡                              (                λ                )                                                        
One reason that these conventional calculations, such as the Kubelka-Munk equation, have not been applicable to graphic design applications is because such applications use ICC profiles to make their color predictions. These ICC profiles use CIELAB data and generally do not contain full spectral information. In this case, the above-discussed conventional calculations cannot easily be used for purposes of modifying profiles, updating profiles, or performing a priori mixing calculations on information obtained from ICC profiles.
Accordingly, a need in the art exists for efficiently and accurately predicting the appearance of mixed colors in the absence of full spectral information.